At present, integrated energy systems have received extensive attention, but there is no basic framework for stability analysis of coupled systems. The injection of a large amount of renewable energy also has a great impact on the stability of the system. This paper focuses on how to analyze the static stability of the coupling system with uncertainty, which mainly considers the uncertainty of wind power generation and photovoltaic power generation and also considers the influence of P2G technology on the whole system. Firstly, this paper analyzes the principles of wind power generation and photovoltaic power generation and constructs the probability model of renewable energy power generation power. Then, the three-point estimation method is used to process the data, and the probability distribution of the unknown quantity is obtained by probabilistic power flow analysis. Finally, the probability distribution of each eigenvalue is obtained by analyzing the sensitivity of the characteristic roots to the voltage. Thus, the static stability of the system is judged. The applicability of proposed methodology is demonstrated by analyzing an integrated IEEE 14-bus power system and a Belgian 20-node gas system in this paper.
With the in-depth study of renewable energy [
The peak period of renewable energy is probably the low valley period of power grid load resulting in great waste. Considering that the reaction is unlikely to be complete, P2G technology will eventually produce a gas mixture of hydrogen and methane [
And, randomness is the uncertainty of exponential value. The generation power of renewable energy depends on the amount of energy at that time, and the amount of renewable energy is affected by many natural factors and is not controllable, which brings uncertain data to the system. This makes it difficult to judge the state of the system. It is very important whether the system can run stably [
At present, there are three methods for calculating probabilistic power flow: fuzzy mathematics method [
Many papers have studied the probabilistic power flow calculation of wind power generation and photovoltaic power generation. In [
The state of the system is often obtained by power flow calculation to judge the static stability of the system. Static stability refers to the ability of a system to operate stably after a small disturbance, which can be used to find the weak points of the system. In order to ensure the safe and reliable operation of the system, it is necessary to analyze the static stability of the system [
Not only the power grid has static stability but also the gas network has static stability. Because the gas transported in the gas network is flammable and explosive, the stability of the gas network is also very important. But, P2G technology will use extra power to electrolyze water to get combustible gas and put the resulting mixture into the gas network. It will lead to changes in gas characteristics specific gravity (SG) and gross calorific value (GCV) and influence the operation of the gas grid. If a more accurate stability analysis of the integrated power-gas System is required, we should further the model of the gas network with gas mixture and calculate the power flow according to the new model. There are several papers on integrated power-gas systems. Yang et al. [
To the best of authors’ knowledge, there is little consideration that the stability of a system with uncertain data, and no consideration that the uncertainty of renewable energy and the consumption of renewable energy by P2G technology’s together. Of course, there also is no consideration that the static stability of integrated power-gas systems static with wind power generation and photovoltaic power generation. To solve these problems, the main contributions of this paper can be concluded as follows: An probabilistic power flow calculation method considering P2G technology is proposed. It not only considers the impact of the uncertainty of renewable energy on the system but also considers the impact of the gas mixture produced by P2G on the gas network. This makes the static stability analysis of the system more practical and more accurate. Based on probabilistic power flow calculation, the probability distribution of the power system static stability probability distribution of power system is analyzed. Considering the influence of uncertain data on power system, the confidence level of system stability can be obtained by analyzing the probability distribution of the unknown quantity. The potential dangers and weak links of power system operation can also be judged through the data. Not only the stability of electric power network but also the stability of gas network is considered. The uncertainty of renewable energy is analyzed, and its influence on the stability of gas network is obtained. In this way, it can effectively judge whether there is pipe blocking phenomenon in the gas network, so as to prevent accidents to some extent.
This paper is described in detail as follows. Treatment of uncertain data on wind and photovoltaic power generation is described in Section
The height of the weather station wind meter may not be the same as the height of the fan wheel shaft, so it is necessary to convert the wind speed measured by the wind meter into the wind speed at the fan wheel shaft height when calculating the wind power generated. The relationship between them can be expressed as
The relationship between the output power of wind power generation and wind speed can be expressed as
Daily exposure hours can be obtained from the data from weather stations. The total amount of daylight radiation throughout the day can be expressed as
Most of the existing studies use peak watt power to calculate the photovoltaic power generation. The daily exposure hours can be converted to peak watt hours and expressed as
The three-point estimation method is the Taylor series expansion of the function
So, the standard deviation of
The uncertain data in the system are processed by the three-point estimation method, and the three pick-point positions of each uncertain node can be obtained. Then, substituting these three points into the power flow calculation, respectively, can obtain the estimated value of each point. Because one of the three pick points for each uncertain data is the mean, so if the number of the uncertain nodes in the system is
In the electric network, in addition to the line parameter resistance and reactance, each node also corresponds to four variables, which are active power, reactive power, voltage amplitude, and voltage phase angle. According to Kirchhoff’s law, the iterative equation of power flow calculation in electric network can be written as
In the gas network, in addition to the line parameters, pipe length, pipe diameter, and friction coefficient, each node also corresponds to two variables, namely, air pressure and gas flow rate. The pressure drop function due to line parameters can be written as
According to Kirchhoff’s law, considering element characteristics and network topology constraints, the flow deviation equation of gas network nodes can be written as
Because the gas mixture makes the SG and GCV in different positions of the gas network different, there is not only one variable of pressure at each gas node; but two variables of SG and GCV need to be increased. Therefore, the known quantities of relaxation nodes in the gas network are pressure, SG, and GCV, and the unknown quantities are gas flow rate, the known quantities of the load nodes in the gas network are the energy requirements, and the unknown quantities are the pressure, SG, and GCV. There will also be nonmixed air source and mixed air source in the gas network. The known quantities of nonmixed air sources are gas flow rate, SG, and GCV, and the unknown quantities are pressure. The known quantities of the mixed air source are the gas flow rate, and the unknown quantities are the pressure, SG, and GCV.
According to the knowledge of fluid mechanics, SG and GCV of each node of gas network can also be obtained by iteration. This paper mainly considers the influence of the gas mixture of natural gas, hydrogen, and methane generated by P2G on the gas network. So, SG and GCV can be expressed as
Therefore, the Jacobian matrix of power flow calculation for the gas mixture system can be expressed as
A confidence interval of a probability sample is an interval estimate of a population parameter of this sample. The confidence interval shows the degree to which the true value of this parameter has a certain probability of falling around the measurement result. The confidence interval gives the confidence of the measured value of the measured parameter, that is, the “certain probability”. This probability is called the confidence level.
For any system, there is no unique state in which it can reliably operate. Instead, there will be a range within which the system can operate stably. The static stability analysis is to judge whether the running state of the system at that time is within this stable range. And, the uncertainty of data will cause the fluctuation of system running state, so it is impossible to directly judge whether the running state of the system can be in a stable range. In this case, whether the running state of the system is within this range becomes a probabilistic problem. To analyze the static stability of such uncertain system is to analyze the probability that its running state is within the stable range. These are confidence intervals and confidence levels in probabilistic knowledge. The confidence interval we choose is the range that the system can operate stably. The confidence level of system stability is the probability that the system operating state is within this confidence interval.
Existing studies have shown that the static stability of the power system can be judged by calculating the eigenvalue of the Jacobian matrix of power flow [
And, the covariance matrix of the characteristic roots can be expressed as
The probability distribution of each node voltage can be obtained by the above formula, so as to determine how much probability the whole power network can run stably.
The gas transmission pressure of natural gas will affect the operating pressure of the pipeline itself. Appropriate operating pressure is an important guarantee to ensure the stable work and safety of the pipeline. When the gas transmission pressure of natural gas is too large or greater than the normal gas transmission pressure, the gas transmission pressure will have a great impact on the pipeline, increase the flow rate of the fluid, and may directly lead to the fall off or rupture of the pipeline interface. If the gas transmission pressure of the pipeline is too small and the pressure is not enough to reach the normal operating pressure, then the gas transmission pressure cannot make the pipeline carry out normal pipeline transportation.
Therefore, in the transportation of the gas network, the pressure value of each node of the gas network has the greatest influence on the safety. The influence of the fluctuation brought by renewable energy on the stability of the gas network can be judged by judging the probability distribution of pressure of each node in the gas network:
In this paper, the feasibility of this method is verified by an integrated IEEE 14-bus power system and a Belgian 20-node system, which is shown in Figure
Integrated IEEE 14-bus system and Belgian 20-node gas system.
SG and GCV of gas sources.
Natural gas | Synthetic natural gas | Hydrogen | |
---|---|---|---|
SG | 0.6048 | 0.58 | 0.0696 |
GCV | 41.04 | 37.4 | 12.75 |
The data used in this paper are from a group of wind power generation with 30 wind turbines. The rated power of each wind turbines is 2.5 MW. The cut in wind speed, rated wind speed, and cut out wind speed are, respectively, 13 m/s, 7.3 m/s, and 13 m/s. The mean value of wind speed data is 5 m/s, and the standard deviation is 8 m/s. Thus, the probability density function of the output power of the wind generator can be obtained, which is shown in Figure
Probability density function of wind photovoltaic power generation.
In this paper, the photovoltaic generator is located at 104.4°
Probability density function of photovoltaic power generation.
Using the three-point estimation method to process the data, we can obtain the three-point location and probability of wind power generation and photovoltaic power generation. And then, plugging those points into the power flow equation can get five sets of results. Finally, the probability distribution of eigenvalues calculated by each power flow can be analyzed. Because the whole power system has 14 nodes, including one slack node, four PV nodes, and nine PQ nodes, there are 22 power flow equations in the power system, namely, 22 characteristic roots. There are nine pairs of conjugate characteristic roots, the 1st and 2nd, the 4th and 5th, the 7th and 8th, the 10th and 11th, the 12th and 13th, the 14th and 15th, the 16th and 17th, the 19th and 20th, and the 21st and 22nd. Since the static stability of the system depends on the real part of each characteristic root, the effect of a pair of conjugate characteristic roots on the stability of the system is the same. The probability distribution of the characteristic root real part can be obtained by analyzing the five groups of characteristic root values, which is shown in Figure
Probability distribution of the eigenvalue.
The impact of renewable energy uncertainty on SG and GCV of each node can be analyzed through the data obtained from the above power flow calculation. Finally, the mean values of SG and GCV at each node is shown in Table
SG and GCV at different nodes.
Node | SG | GCV | Node | SG | GCV |
---|---|---|---|---|---|
1 | 0.6048 | 41.04 | 11 | 0.58 | 37.4 |
2 | 0.5972 | 39.9413 | 12 | 0.58 | 37.4 |
3 | 0.5972 | 39.9413 | 13 | 0.58 | 37.398 |
4 | 0.5972 | 39.9413 | 14 | 0.5883 | 38.6338 |
5 | 0.58 | 37.4 | 15 | 0.5883 | 38.6338 |
6 | 0.5861 | 38.2952 | 16 | 0.5883 | 38.6338 |
7 | 0.5972 | 39.9413 | 17 | 0.58 | 37.4 |
8 | 0.58 | 37.4 | 18 | 0.58 | 37.4 |
9 | 0.58 | 37.4 | 19 | 0.58 | 37.4 |
10 | 0.58 | 37.4 | 20 | 0.58 | 37.4 |
SG at node 14.
GCV at node 14.
By analyzing the pressure value of each node in the gas network, the probability distribution can be obtained, which is shown in Figure
Probability distribution of the eigenvalue.
Probability distribution of pressure at node 3.
Figure
Comparison among Nodes 3, 19, and 20.
This paper constructed a coupling network model considering renewable energy generation and P2G technology and did a static stability analysis of this model. This model takes into account the influence of renewable power generation uncertainty on the system. It also takes into account the impact of P2G technology on the gas characteristics specific gravity and gross calorific value of the whole network. In this paper, the static stability of this model is analyzed by probabilistic power flow calculation and characteristic root sensitivity method. The influence of data uncertainty on the stability of power network and gas network is analyzed, respectively. The confidence level of the system can be obtained by determining the confidence interval of power network and gas network. Thus, the potential danger and weak link of the system can be further judged. The feasibility of this method is verified by simulation based on actual data. The effects of the randomness and intermittency of renewable energy on the stability of the system are visually demonstrated.
The data used to support the findings of this study are included within the article.
The authors declare they have no conflicts of interest.
This work was supported by the National Key R&D Program of China under grant (2018YFA0702200), the Key Projects of National Natural Science Foundation of China (U20A20190), the National Natural Science Foundation of China (62073065), and the Liaoning Province to Revitalize the Liao Talents Plan (XLYC1802046).